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Simplifying 32 = 6x2 + -12x + -48 Reorder the terms: 32 = -48 + -12x + 6x2 Solving 32 = -48 + -12x + 6x2 Solving for variable 'x'. Combine like terms: 32 + 48 = 80 80 + 12x + -6x2 = -48 + -12x + 6x2 + 48 + 12x + -6x2 Reorder the terms: 80 + 12x + -6x2 = -48 + 48 + -12x + 12x + 6x2 + -6x2 Combine like terms: -48 + 48 = 0 80 + 12x + -6x2 = 0 + -12x + 12x + 6x2 + -6x2 80 + 12x + -6x2 = -12x + 12x + 6x2 + -6x2 Combine like terms: -12x + 12x = 0 80 + 12x + -6x2 = 0 + 6x2 + -6x2 80 + 12x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 80 + 12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + 6x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + 6x + -3x2)' equal to zero and attempt to solve: Simplifying 40 + 6x + -3x2 = 0 Solving 40 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -13.33333333 + -2x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -2x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -2x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -2x + x2 = 0 + 13.33333333 -2x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -2x + x2 = 13.33333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 13.33333333 + 1 Reorder the terms: 1 + -2x + x2 = 13.33333333 + 1 Combine like terms: 13.33333333 + 1 = 14.33333333 1 + -2x + x2 = 14.33333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 14.33333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (x + -1) equal to 3.785938897 and -3.785938897.Subproblem 1
x + -1 = 3.785938897 Simplifying x + -1 = 3.785938897 Reorder the terms: -1 + x = 3.785938897 Solving -1 + x = 3.785938897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.785938897 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.785938897 + 1 x = 3.785938897 + 1 Combine like terms: 3.785938897 + 1 = 4.785938897 x = 4.785938897 Simplifying x = 4.785938897Subproblem 2
x + -1 = -3.785938897 Simplifying x + -1 = -3.785938897 Reorder the terms: -1 + x = -3.785938897 Solving -1 + x = -3.785938897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.785938897 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.785938897 + 1 x = -3.785938897 + 1 Combine like terms: -3.785938897 + 1 = -2.785938897 x = -2.785938897 Simplifying x = -2.785938897Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.785938897, -2.785938897}Solution
x = {4.785938897, -2.785938897}
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